An explicit solution for optimal investment in Heston model

TL;DR

This paper derives an explicit solution for the optimal investment problem within the Heston stochastic volatility model, extending the class of solvable stochastic control problems in finance.

Contribution

It provides the first exact analytical solution for the optimal investment problem under the Heston model, a widely used stochastic volatility framework.

Findings

Explicit solution for Heston model investment problem

Enhances understanding of optimal control under stochastic volatility

Facilitates practical implementation of optimal investment strategies

Abstract

In this paper we consider a variation of the Merton's problem with added stochastic volatility and finite time horizon. It is known that the corresponding optimal control problem may be reduced to a linear parabolic boundary problem under some assumptions on the underlying process and the utility function. The resulting parabolic PDE is often quite difficult to solve, even when it is linear. The present paper contributes to the pool of explicit solutions for stochastic optimal control problems. Our main result is the exact solution for optimal investment in Heston model.